Hi and welcome,
Your puppy is very much a baby and does not have any control over when he needs to relieve himself,as you rightly said this can take up to six months maybe longer.
You are dong the right thing by praising and rewarding him after he has been in the right place,I would only use one word though not both busy and good,maybe just "busy".

Have you thought of taking the crate into your room at night so you can take him outside if the need arises say at 3 am,going all night is too much to expect off such a young puppy.
I did this with both mine would put them out last thing 11pm,settle them in their crates in our room and if they cried during the night would take them out to relieve themselves extending the time by a few minutes each night.

When he soils in the wrong place pick him up place him outside and clean the area with bio washing powder to get rid of the smell.I tend not to use newspaper or training pads as I think it's takes longer to train a puppy as you are giving the signal it's ok to go indoors.

Remember young puppies need to go out,every half an hour to an hour,after play,feeding,sleep etc.

Good Luck!